Asymptotic Behavior of Solutions for Neutral Dynamic Equations on Time Scales

where T is a time scale unbounded above, the variable delays k, : [t0,∞)T → T are nondecreasing with k(t), (t) < t for all t ∈ [t0,∞)T such that limt→∞ k(t), (t)=∞. The coefficient functions p,q : T→R are right-dense continuous with p bounded and q ≥ 0. To clarify some notation, take −1(t) := sup{s : (s) ≤ t}, −(n+1)(t)= −1( −n(t)) for t ∈ [ (t0),∞)T, and n+1(t) = ( n(t)) for t ∈ [ −3(t0),∞)T. For p and k above, let Ω be the linear set of all functions given by Ω := x : T→R : x(t)− p(t)xk(t)Δ ∈ Crd ([ t0,∞ ) T;R )} ; (1.2)